Simple Equations

Excerpts

Simple Equations
An equation is a statement in symbols that two expressions stand for the same number.
Simple Equations
Thus, $a + b = b + a$, which is true for *all values* of $a$ and $b$, is an *identical equation*, and $3x + 2 = 8$, which is true only when $x$ stands for $2$, is an *equation of condition*
Simple Equations
Any term may be transposed from one side of an equation to the other, provided its sign is changed.
Simple Equations
When the root is substituted for its symbol in the given equation, and the equation reduces to an *identity*, the root is said to be **verified**.
Simple Equations
Remember that $x$ must not be put for money, length, time, weight, etc., but for the **required number** of *specified units* of money, length, time, weight, etc.
Simple Equations
Now, we know *what* James had. He had oranges, and we are to discover simply the *number* of oranges he had.

Equations

Simple Equations
a + b = b + a
Adding two numbers gives the same result in either order, so this equation holds for all values of a and b.
Simple Equations
3x + 2 = 8
The statement that 3x + 2 and 8 stand for the same number, which is true only when x stands for 2, so it is an equation of condition.
Simple Equations
ax + b = c
The general form of a simple equation in x, in which a, b and c are known numbers and x is the unknown.
Simple Equations
x = a - b
Solving x + b = a by subtracting b from both sides gives x equal to a minus b.
Simple Equations
x = a + b
Solving x - b = a by adding b to both sides gives x equal to a plus b.

Problems

Exercise 9

Exercise 9, problem 1, p. 24
$3x = x + 8$.
Printed answer:
- $4$.
verified: the printed answer passed a computed check
How it was checked
- solve: passes 4
On the STU-32 (STU, rpn):
```
8 ENTER 3 ENTER 1 −
```
```
÷
```
Calculator: +4E+0; the book prints 4. Run on the calculator core at firmware 628c96c.
Exercise 9, problem 10, p. 24
$3(x - 2) = 2(x - 1)$.
Printed answer:
- $4$.
verified: the printed answer passed a computed check
How it was checked
- solve: passes 4
On the STU-32 (STU, rpn):
```
3 ENTER 2 × 2 ENTER 1 × −
```
```
3 ENTER 2 − ÷
```
Calculator: +4E+0; the book prints 4. Run on the calculator core at firmware 628c96c.
Exercise 9, problem 11, p. 24
$2x + 3 = 16 - (2x - 3)$.
Printed answer:
- $4$.
verified: the printed answer passed a computed check
How it was checked
- solve: passes 4
On the STU-32 (STU, rpn):
```
16 ENTER 2 ENTER 2 + ÷
```
Calculator: +4E+0; the book prints 4. Run on the calculator core at firmware 628c96c.
Exercise 9, problem 12, p. 24
$19x - 3 = 2(7 + x)$.
Printed answer:
- $1$.
verified: the printed answer passed a computed check
How it was checked
- solve: passes 1
On the STU-32 (STU, rpn):
```
2 ENTER 7 × 3 +
```
```
19 ENTER 2 −
```
```
÷
```
Calculator: +1E+0; the book prints 1. Run on the calculator core at firmware 628c96c.
Exercise 9, problem 13, p. 24
$7x - 70 = 5x - 20$.
Printed answer:
- $25$.
verified: the printed answer passed a computed check
How it was checked
- solve: passes 25
On the STU-32 (STU, rpn):
```
70 ENTER 20 −
```
```
7 ENTER 5 − ÷
```
Calculator: +25E+0; the book prints 25. Run on the calculator core at firmware 628c96c.
Exercise 9, problem 14, p. 24
$2x - 22 = 108 - 2x$.
Printed answer:
- $32\frac{1}{2}$.
verified: the printed answer passed a computed check
How it was checked
- solve: passes Rational(65, 2)
On the STU-32 (STU, rpn):
```
2 ENTER 2 +
```
```
108 ENTER 22 +
```
```
x↔y ÷
```
Calculator: +325E-1; the book prints 65/2. Run on the calculator core at firmware 628c96c.
Exercise 9, problem 15, p. 24
$2(x + 5) + 5(x - 4) = 32$.
Printed answer:
- $6$.
verified: the printed answer passed a computed check
How it was checked
- solve: passes 6
On the STU-32 (STU, rpn):
```
32 ENTER 2 ENTER 5 × 5 ENTER 4 × − −
```
```
2 ENTER 5 + ÷
```
Calculator: +6E+0; the book prints 6. Run on the calculator core at firmware 628c96c.
Exercise 9, problem 16, p. 24
$2(3x - 25) = 10$.
Printed answer:
- $10$.
verified: the printed answer passed a computed check
How it was checked
- solve: passes 10
On the STU-32 (STU, rpn):
```
10 ENTER 2 ÷
```
```
25 +
```
```
3 ÷
```
Calculator: +10E+0; the book prints 10. Run on the calculator core at firmware 628c96c.
Exercise 9, problem 17, p. 24
$33x - 70 = 3x + 20$.
Printed answer:
- $3$.
verified: the printed answer passed a computed check
How it was checked
- solve: passes 3
On the STU-32 (STU, rpn):
```
70 ENTER 20 +
```
```
33 ENTER 3 −
```
```
÷
```
Calculator: +3E+0; the book prints 3. Run on the calculator core at firmware 628c96c.
Exercise 9, problem 18, p. 24
$4(1 + x) + 3(2 + x) = 17$.
Printed answer:
- $1$.
verified: the printed answer passed a computed check
How it was checked
- solve: passes 1
On the STU-32 (STU, rpn):
```
4 ENTER 1 × 3 ENTER 2 × +
```
```
17 x↔y −
```
```
4 ENTER 3 + ÷
```
Calculator: +1E+0; the book prints 1. Run on the calculator core at firmware 628c96c.
Exercise 9, problem 19, p. 24
$8x - (x + 2) = 47$.
Printed answer:
- $7$.
verified: the printed answer passed a computed check
How it was checked
- solve: passes 7
On the STU-32 (STU, rpn):
```
47 ENTER 2 +
```
```
8 ENTER 1 − ÷
```
Calculator: +7E+0; the book prints 7. Run on the calculator core at firmware 628c96c.
Exercise 9, problem 2, p. 24
$3x = 2x + 5$.
Printed answer:
- $5$.
verified: the printed answer passed a computed check
How it was checked
- solve: passes 5
On the STU-32 (STU, rpn):
```
5 ENTER 3 ENTER 2 − ÷
```
Calculator: +5E+0; the book prints 5. Run on the calculator core at firmware 628c96c.
Exercise 9, problem 20, p. 24
$3(x - 2) = 50 - (2x - 9)$.
Printed answer:
- $13$.
verified: the printed answer passed a computed check
How it was checked
- solve: passes 13
On the STU-32 (STU, rpn):
```
3 ENTER 2 × 9 +
```
```
50 +
```
```
3 ENTER 2 +
```
```
÷
```
Calculator: +13E+0; the book prints 13. Run on the calculator core at firmware 628c96c.
Exercise 9, problem 21, p. 24
$2x - (3 + 4x - 3x + 5) = 4$.
Printed answer:
- $12$.
verified: the printed answer passed a computed check
How it was checked
- solve: passes 12
On the STU-32 (STU, rpn):
```
4 ENTER 3 ENTER 5 + +
```
Calculator: +12E+0; the book prints 12. Run on the calculator core at firmware 628c96c.
Exercise 9, problem 22, p. 24
$5(2 - x) + 7x - 21 = x + 3$.
Printed answer:
- $14$.
verified: the printed answer passed a computed check
How it was checked
- solve: passes 14
On the STU-32 (STU, rpn):
```
3 ENTER 21 +
```
```
5 ENTER 2 × −
```
```
7 ENTER 5 − 1 − ÷
```
Calculator: +14E+0; the book prints 14. Run on the calculator core at firmware 628c96c.
Exercise 9, problem 23, p. 24
$3(x - 2) + 2(x - 3) + (x - 4) = 3x + 5$.
Printed answer:
- $7$.
verified: the printed answer passed a computed check
How it was checked
- solve: passes 7
On the STU-32 (STU, rpn):
```
3 ENTER 2 × 2 ENTER 3 × + 4 + 5 +
```
```
3 ENTER 2 + 1 + 3 − ÷
```
Calculator: +7E+0; the book prints 7. Run on the calculator core at firmware 628c96c.
Exercise 9, problem 24, p. 24
$x + 1 + x + 2 + x + 4 = 2x + 12$.
Printed answer:
- $5$.
verified: the printed answer passed a computed check
How it was checked
- solve: passes 5
On the STU-32 (STU, rpn):
```
12 ENTER 1 ENTER 2 + 4 +
```
```
−
```
Calculator: +5E+0; the book prints 5. Run on the calculator core at firmware 628c96c.
Exercise 9, problem 25, p. 24
$(2x - 5) - (x - 4) + (x - 3) = x - 4$.
Printed answer:
- $0$.
verified: the printed answer passed a computed check
How it was checked
- solve: passes 0
On the STU-32 (STU, rpn):
```
5 +/− ENTER 4 + ENTER 3 −
```
```
4 +/− x↔y −
```
```
2 ENTER 1 − ÷
```
Calculator: +0E-6176; the book prints 0. Run on the calculator core at firmware 628c96c.
Exercise 9, problem 26, p. 24
$4 - 5x - (1 - 8x) = 63 - x$.
Printed answer:
- $15$.
verified: the printed answer passed a computed check
How it was checked
- solve: passes 15
Exercise 9, problem 27, p. 24
$3x - (x + 10) - (x - 3) = 14 - x$.
Printed answer:
- $10\frac{1}{2}$.
verified: the printed answer passed a computed check
How it was checked
- solve: passes Rational(21, 2)
Exercise 9, problem 28, p. 24
$x^{2} - 2x - 3 = x^{2} - 3x + 1$.
Printed answer:
- $4$.
verified: the printed answer passed a computed check
How it was checked
- solve: passes 4
On the STU-32 (STU, rpn):
```
1 ENTER 3 +
```
Calculator: +4E+0; the book prints 4. Run on the calculator core at firmware 628c96c.
Exercise 9, problem 29, p. 24
$(x^{2} - 9) - (x^{2} - 16) + x = 10$.
Printed answer:
- $3$.
verified: the printed answer passed a computed check
How it was checked
- solve: passes 3
On the STU-32 (STU, rpn):
```
16 ENTER 9 −
```
```
10 x↔y −
```
Calculator: +3E+0; the book prints 3. Run on the calculator core at firmware 628c96c.
Exercise 9, problem 3, p. 24
$3x + 4 = x + 10$.
Printed answer:
- $3$.
verified: the printed answer passed a computed check
How it was checked
- solve: passes 3
On the STU-32 (STU, rpn):
```
10 ENTER 4 −
```
```
3 ENTER 1 −
```
```
÷
```
Calculator: +3E+0; the book prints 3. Run on the calculator core at firmware 628c96c.
Exercise 9, problem 30, p. 24
$x^{2} + 8x - (x^{2} - x - 2) = 5(x + 3) + 3$.
Printed answer:
- $4$.
verified: the printed answer passed a computed check
How it was checked
- solve: passes 4
On the STU-32 (STU, rpn):
```
5 ENTER 3 × 3 + 2 −
```
```
8 ENTER 1 + 5 − ÷
```
Calculator: +4E+0; the book prints 4. Run on the calculator core at firmware 628c96c.
Exercise 9, problem 31, p. 24
$x^{2} + x - 2 + x^{2} + 2x - 3 = 2x^{2} - 7x - 1$.
Printed answer:
- $\frac{2}{5}$.
verified: the printed answer passed a computed check
How it was checked
- solve: passes Rational(2, 5)
On the STU-32 (STU, rpn):
```
2 ENTER 3 + 1 −
```
```
3 ENTER 7 + ÷
```
Calculator: +4E-1; the book prints 2/5. Run on the calculator core at firmware 628c96c.
Exercise 9, problem 32, p. 24
$10x - (x - 5) = 2x + 47$.
Printed answer:
- $6$.
verified: the printed answer passed a computed check
How it was checked
- solve: passes 6
On the STU-32 (STU, rpn):
```
47 ENTER 5 −
```
```
10 ENTER 1 − 2 − ÷
```
Calculator: +6E+0; the book prints 6. Run on the calculator core at firmware 628c96c.
Exercise 9, problem 33, p. 24
$7x - 5 - (6 - 8x) + 2 = 3x - 7 + 106$.
Printed answer:
- $9$.
verified: the printed answer passed a computed check
How it was checked
- solve: passes 9
On the STU-32 (STU, rpn):
```
5 ENTER 6 + 2 − 7 − 106 +
```
```
ENTER 7 ENTER 8 + 3 −
```
```
÷
```
Calculator: +9E+0; the book prints 9. Run on the calculator core at firmware 628c96c.
Exercise 9, problem 34, p. 24
$6x + 3 - (3x + 2) = (2x - 1) + 9$.
Printed answer:
- $7$.
verified: the printed answer passed a computed check
How it was checked
- solve: passes 7
On the STU-32 (STU, rpn):
```
9 ENTER 1 − 3 ENTER 2 − −
```
```
6 ENTER 3 − 2 − ÷
```
Calculator: +7E+0; the book prints 7. Run on the calculator core at firmware 628c96c.
Exercise 9, problem 35, p. 24
$3(x + 10) + 4(x + 20) + 5x - 170 = 15 - 3x$.
Printed answer:
- $5$.
verified: the printed answer passed a computed check
How it was checked
- solve: passes 5
On the STU-32 (STU, rpn):
```
15 ENTER 3 ENTER 10 × − 4 ENTER 20 × − 170 +
```
```
3 ENTER 4 + 5 + 3 + ÷
```
Calculator: +5E+0; the book prints 5. Run on the calculator core at firmware 628c96c.
Exercise 9, problem 36, p. 24
$20 - x + 4(x - 1) - (x - 2) = 30$.
Printed answer:
- $6$.
verified: the printed answer passed a computed check
How it was checked
- solve: passes 6
On the STU-32 (STU, rpn):
```
20 ENTER 4 ENTER 1 × − 2 +
```
```
30 x↔y − 2 ÷
```
Calculator: +6E+0; the book prints 6. Run on the calculator core at firmware 628c96c.
Exercise 9, problem 37, p. 24
$5x + 3 - (2x - 2) + (1 - x) = 6(9 - x)$.
Printed answer:
- $6$.
verified: the printed answer passed a computed check
How it was checked
- solve: passes 6
On the STU-32 (STU, rpn):
```
6 ENTER 9 ×
```
```
3 ENTER 2 +/− − 1 +
```
```
−
```
```
5 ENTER 2 − 1 − 6 +
```
```
÷
```
Calculator: +6E+0; the book prints 6. Run on the calculator core at firmware 628c96c.
Exercise 9, problem 4, p. 24
$4x + 6 = x + 9$.
Printed answer:
- $1$.
verified: the printed answer passed a computed check
How it was checked
- solve: passes 1
Exercise 9, problem 5, p. 24
$7x - 19 = 5x + 7$.
Printed answer:
- $13$.
verified: the printed answer passed a computed check
How it was checked
- solve: passes 13
On the STU-32 (STU, rpn):
```
19 ENTER 7 +
```
```
7 ENTER 5 −
```
```
÷
```
Calculator: +13E+0; the book prints 13. Run on the calculator core at firmware 628c96c.
Exercise 9, problem 6, p. 24
$3(x - 2) = 2(x - 3)$.
Printed answer:
- $0$.
verified: the printed answer passed a computed check
How it was checked
- solve: passes 0
On the STU-32 (STU, rpn):
```
3 ENTER 2 ×
```
```
2 ENTER 3 × −
```
Calculator: +0E-6176; the book prints 0. Run on the calculator core at firmware 628c96c.
Exercise 9, problem 7, p. 24
$8x + 7 = 4x + 27$.
Printed answer:
- $5$.
verified: the printed answer passed a computed check
How it was checked
- solve: passes 5
On the STU-32 (STU, rpn):
```
27 ENTER 7 −
```
```
8 ENTER 4 −
```
```
÷
```
Calculator: +5E+0; the book prints 5. Run on the calculator core at firmware 628c96c.
Exercise 9, problem 8, p. 24
$3x + 10 = x + 20$.
Printed answer:
- $5$.
verified: the printed answer passed a computed check
How it was checked
- solve: passes 5
On the STU-32 (STU, rpn):
```
20 ENTER 10 −
```
```
3 ENTER 1 −
```
```
÷
```
Calculator: +5E+0; the book prints 5. Run on the calculator core at firmware 628c96c.
Exercise 9, problem 9, p. 24
$5(x - 2) = 3x + 4$.
Printed answer:
- $7$.
verified: the printed answer passed a computed check
How it was checked
- solve: passes 7
On the STU-32 (STU, rpn):
```
4 ENTER 5 ENTER 2 × +
```
```
5 ENTER 3 − ÷
```
Calculator: +7E+0; the book prints 7. Run on the calculator core at firmware 628c96c.

Exercise 10

Exercise 10, problem 1, p. 27
If a number is multiplied by $9$, the product is $270$. Find the number.
Printed answer:
- $30$.
verified: the printed answer passed a computed check
How it was checked
- solve: passes, with the problem read into an equation {x: 30}
On the STU-32 (STU, rpn):
```
270 ENTER 9 ÷
```
Calculator: +30E+0; the book prints 30. Run on the calculator core at firmware 628c96c.
Exercise 10, problem 10, p. 27
One number is $4$ times another, and their difference is $30$. Find the numbers.
Printed answer:
- $10$, $40$.
verified: the printed answer passed a computed check
How it was checked
- solve: passes, with the problem read into an equation {x: 40, y: 10}
Exercise 10, problem 11, p. 27
The sum of two numbers is $36$, and one of them exceeds twice the other by $6$. Find the numbers.
Printed answer:
- $26$, $10$.
verified: the printed answer passed a computed check
How it was checked
- solve: passes, with the problem read into an equation {x: 26, y: 10}
Exercise 10, problem 12, p. 27
The sum of two numbers is $40$, and $5$ times the smaller exceeds $2$ times the greater by $25$. Find the numbers.
Printed answer:
- $25$, $15$.
verified: the printed answer passed a computed check
How it was checked
- solve: passes, with the problem read into an equation {x: 25, y: 15}
Exercise 10, problem 13, p. 27
The number $30$ is divided into two parts such that $4$ times the greater part exceeds $5$ times the smaller part by $30$. Find the parts.
Printed answer:
- $10$, $20$.
verified: the printed answer passed a computed check
How it was checked
- solve: passes, with the problem read into an equation {x: 20, y: 10}
Exercise 10, problem 14, p. 27
The sum of two numbers is $27$, and twice the greater number increased by $3$ times the less is $61$. Find the numbers.
Printed answer:
- $7$, $20$.
verified: the printed answer passed a computed check
How it was checked
- solve: passes, with the problem read into an equation {x: 20, y: 7}
Exercise 10, problem 15, p. 27
The sum of two numbers is $32$, and five times the smaller is $3$ times the greater number. Find the numbers.
Printed answer:
- $12$, $20$.
verified: the printed answer passed a computed check
How it was checked
- solve: passes, with the problem read into an equation {x: 20, y: 12}
Exercise 10, problem 2, p. 27
If the sum of the ages of a father and son is $60$ years, and the father is $5$ times as old as the son, what is the age of each?
Printed answer:
- Son, $10$ yr.; father, $50$ yr.
verified: the printed answer passed a computed check
How it was checked
- solve: passes, with the problem read into an equation {s: 10, f: 50}
Exercise 10, problem 3, p. 27
The sum of two numbers is $91$, and the greater is $6$ times the less. Find the numbers.
Printed answer:
- $78$, $13$.
verified: the printed answer passed a computed check
How it was checked
- solve: passes, with the problem read into an equation {x: 78, y: 13}
Exercise 10, problem 4, p. 27
A tree $90$ feet high was broken so that the part broken off was $8$ times the length of the part left standing. Find the length of each part.
Printed answer:
- $80$ ft. broken off; $10$ ft. standing.
verified: the printed answer passed a computed check
How it was checked
- solve: passes, with the problem read into an equation {b: 80, s: 10}
Exercise 10, problem 5, p. 27
The difference of two numbers is $7$, and their sum is $53$. Find the numbers.
Printed answer:
- $23$, $30$.
verified: the printed answer passed a computed check
How it was checked
- solve: passes, with the problem read into an equation {x: 30, y: 23}
Exercise 10, problem 6, p. 27
The difference of two numbers is $12$, and their sum is $84$. Find the numbers.
Printed answer:
- $36$, $48$.
verified: the printed answer passed a computed check
How it was checked
- solve: passes, with the problem read into an equation {x: 48, y: 36}
Exercise 10, problem 7, p. 27
Divide $35$ into two parts so that one part shall be greater by $5$ than the other part.
Printed answer:
- $15$, $20$.
verified: the printed answer passed a computed check
How it was checked
- solve: passes, with the problem read into an equation {x: 20, y: 15}
Exercise 10, problem 8, p. 27
Three times a given number is equal to the number increased by $40$. Find the number.
Printed answer:
- $20$.
verified: the printed answer passed a computed check
How it was checked
- solve: passes, with the problem read into an equation {x: 20}
On the STU-32 (STU, rpn):
```
40 ENTER 3 ENTER 1 −
```
```
÷
```
Calculator: +20E+0; the book prints 20. Run on the calculator core at firmware 628c96c.
Exercise 10, problem 9, p. 27
Three times a given number diminished by $24$ is equal to the given number. Find the number.
Printed answer:
- $12$.
verified: the printed answer passed a computed check
How it was checked
- solve: passes, with the problem read into an equation {x: 12}
On the STU-32 (STU, rpn):
```
24 ENTER 3 ENTER 1 −
```
```
÷
```
Calculator: +12E+0; the book prints 12. Run on the calculator core at firmware 628c96c.

Exercise 11

Exercise 11, problem 1, p. 29
A farmer sold a horse and a cow for $$210$. He sold the horse for four times as much as the cow. How much did he get for each?
Printed answer:
- Cow, $$42$; horse, $$168$.
verified: the printed answer passed a computed check
How it was checked
- solve: passes {c: 42, h: 168}
Exercise 11, problem 10, p. 29
A man $50$ years old has a son $10$ years old. In how many years will the father be three times as old as the son?
Printed answer:
- $10$.
verified: the printed answer passed a computed check
How it was checked
- solve: passes 10
On the STU-32 (STU, rpn):
```
50 ENTER 3 ENTER 10 × −
```
```
3 ENTER 1 −
```
```
÷
```
Calculator: +10E+0; the book prints 10. Run on the calculator core at firmware 628c96c.
Exercise 11, problem 11, p. 29
A has $$100$, and B has $$20$. How much must A give B in order that they may each have the same sum?
Printed answer:
- $$40$.
verified: the printed answer passed a computed check
How it was checked
- solve: passes 40
On the STU-32 (STU, rpn):
```
100 ENTER 20 −
```
```
2 ÷
```
Calculator: +40E+0; the book prints 40. Run on the calculator core at firmware 628c96c.
Exercise 11, problem 12, p. 29
A banker paid $$63$ in $5$-dollar bills and $2$-dollar bills. He paid just as many $5$-dollar bills as $2$-dollar bills. How many bills of each kind did he pay?
Printed answer:
- $9$.
verified: the printed answer passed a computed check
How it was checked
- solve: passes 9
On the STU-32 (STU, rpn):
```
63 ENTER 5 ENTER 2 + ÷
```
Calculator: +9E+0; the book prints 9. Run on the calculator core at firmware 628c96c.
Exercise 11, problem 2, p. 29
Three times the excess of a certain number over $6$ is equal to the number plus $144$. Find the number.
Printed answer:
- $81$.
verified: the printed answer passed a computed check
How it was checked
- solve: passes 81
On the STU-32 (STU, rpn):
```
144 ENTER 3 ENTER 6 × +
```
```
3 ENTER 1 − ÷
```
Calculator: +81E+0; the book prints 81. Run on the calculator core at firmware 628c96c.
Exercise 11, problem 3, p. 29
Thirty-one times a certain number is as much above $40$ as nine times the number is below $40$. Find the number.
Printed answer:
- $2$.
verified: the printed answer passed a computed check
How it was checked
- solve: passes 2
On the STU-32 (STU, rpn):
```
40 ENTER 40 +
```
```
31 ENTER 9 +
```
```
÷
```
Calculator: +2E+0; the book prints 2. Run on the calculator core at firmware 628c96c.
Exercise 11, problem 4, p. 29
Two numbers differ by $10$, and their sum is equal to seven times their difference. Find the numbers.
Printed answer:
- $30$, $40$.
verified: the printed answer passed a computed check
How it was checked
- solve: passes {x: 40, y: 30}
Exercise 11, problem 5, p. 29
Find three consecutive numbers, $x$, $x + 1$, and $x + 2$, whose sum is $78$.
Printed answer:
- $25$, $26$, $27$.
unverified: no computed check settled this one (yet)
How it was checked
- solve: the printed answer does not match the problem [25, 26, 27]
Exercise 11, problem 6, p. 29
Find five consecutive numbers whose sum is $35$.
Printed answer:
- $5$, $6$, $7$, $8$, $9$.
verified: the printed answer passed a computed check
How it was checked
- solve: passes 5
Exercise 11, problem 7, p. 29
The sum of the ages of A and B is $40$ years, and $10$ years hence A will be twice as old as B. Find their present ages.
Printed answer:
- A, $30$ yr.; B, $10$ yr.
verified: the printed answer passed a computed check
How it was checked
- solve: passes {A: 30, B: 10}
Exercise 11, problem 8, p. 29
A father is four times as old as his son, and in $5$ years he will be only three times as old. Find their present ages.
Printed answer:
- Father, $40$ yr., son, $10$ yr.
verified: the printed answer passed a computed check
How it was checked
- solve: passes {F: 40, S: 10}
Exercise 11, problem 9, p. 29
One man is $60$ years old, and another man is $50$ years. How many years ago was the first man twice as old as the second?
Printed answer:
- $40$.
verified: the printed answer passed a computed check
How it was checked
- solve: passes 40
On the STU-32 (STU, rpn):
```
2 ENTER 50 ×
```
```
60 −
```
Calculator: +40E+0; the book prints 40. Run on the calculator core at firmware 628c96c.

Exercise 12

Exercise 12, problem 1, p. 30
In a company of $90$ persons, composed of men, women, and children, there are three times as many children as men, and twice as many women as men. How many are there of each?
Printed answer:
- $15$ men; $30$ women; $45$ children.
verified: the printed answer passed a computed check
How it was checked
- solve: passes, with the problem read into an equation {m: 15, w: 30, c: 45}
Exercise 12, problem 2, p. 30
Find the number whose double exceeds $70$ by as much as the number itself is less than $80$.
Printed answer:
- $50$.
verified: the printed answer passed a computed check
How it was checked
- solve: passes, with the problem read into an equation 50
On the STU-32 (STU, rpn):
```
80 ENTER 70 +
```
```
2 ENTER 1 +
```
```
÷
```
Calculator: +50E+0; the book prints 50. Run on the calculator core at firmware 628c96c.
Exercise 12, problem 3, p. 30
A farmer employed two men to build $112$ rods of wall. One of them built on the average $4$ rods a day, and the other $3$ rods a day. How many days did they work?
Printed answer:
- $16$.
verified: the printed answer passed a computed check
How it was checked
- solve: passes, with the problem read into an equation 16
On the STU-32 (STU, rpn):
```
112 ENTER 4 ENTER 3 + ÷
```
Calculator: +16E+0; the book prints 16. Run on the calculator core at firmware 628c96c.
Exercise 12, problem 4, p. 30
Two men travel in *opposite* directions, one $30$ miles a day, and the other $20$ miles a day. In how many days will they be $350$ miles apart?
Printed answer:
- $7$.
verified: the printed answer passed a computed check
How it was checked
- solve: passes, with the problem read into an equation 7
Exercise 12, problem 5, p. 30
Two men travel in the same direction, one $30$ miles a day, and the other $20$ miles a day. In how many days will they be $350$ miles apart?
Printed answer:
- $35$.
verified: the printed answer passed a computed check
How it was checked
- solve: passes, with the problem read into an equation 35
On the STU-32 (STU, rpn):
```
350 ENTER 30 ENTER 20 −
```
```
÷
```
Calculator: +35E+0; the book prints 35. Run on the calculator core at firmware 628c96c.
Exercise 12, problem 6, p. 30
A man bought $3$ equal lots of hay for $$408$. For the first lot he gave $$17$ a ton, for the second $$16$, for the third $$18$. How many tons did he buy in all?
Printed answer:
- $24$.
verified: the printed answer passed a computed check
How it was checked
- solve: passes, with the problem read into an equation 24
Exercise 12, problem 7, p. 30
A farmer sold a quantity of wood for $$84$, one half of it at $$3$ a cord, and the other half at $$4$ a cord. How many cords did he sell?
Printed answer:
- $24$.
verified: the printed answer passed a computed check
How it was checked
- solve: passes, with the problem read into an equation 24
Exercise 12, problem 8, p. 30
If $2x - 3$ stands for $29$, for what number will $4 + x$ stand?
Printed answer:
- $20$.
verified: the printed answer passed a computed check
How it was checked
- solve: passes, with the problem read into an equation 20
On the STU-32 (STU, rpn):
```
29 ENTER 3 + 2 ÷
```
```
4 +
```
Calculator: +20E+0; the book prints 20. Run on the calculator core at firmware 628c96c.
Exercise 12, problem 9, p. 30
At an election two opposing candidates received together $2044$ votes, and one received $104$ more votes than the other. How many votes did each candidate receive?
Printed answer:
- $970$; $1074$.
verified: the printed answer passed a computed check
How it was checked
- solve: passes, with the problem read into an equation {x: 970, y: 1074}

Exercise 13

Exercise 13, problem 1, p. 31
A man walks $4$ miles an hour for $x$ hours, and another man walks $3$ miles an hour for $x + 2$ hours. If they each walk the same distance, how many miles does each walk?
Printed answer:
- $24$.
verified: the printed answer passed a computed check
How it was checked
- solve: passes, with the problem read into an equation {d: 24}
On the STU-32 (STU, rpn):
```
3 ENTER 2 ×
```
```
4 ENTER 3 − ÷
```
```
4 ×
```
Calculator: +24E+0; the book prints 24. Run on the calculator core at firmware 628c96c.
Exercise 13, problem 2, p. 31
A has twice as much money as B; but if A gives B $$30$, it will take twice as much as A has left to equal B’s. How much money has each?
Printed answer:
- A, $$60$; B, $$30$.
verified: the printed answer passed a computed check
How it was checked
- solve: passes, with the problem read into an equation {a: 60, b: 30}
Exercise 13, problem 3, p. 31
I have $$12.75$ in two-dollar bills and twenty-five cent pieces, and I have twice as many bills as twenty-five cent pieces. How many have I of each?
Printed answer:
- $$3$ quarters; $6$ bills.
verified: the printed answer passed a computed check
How it was checked
- solve: passes, with the problem read into an equation {q: 3, b: 6}
Exercise 13, problem 4, p. 31
I have in mind a certain number. If this number is diminished by $8$ and the remainder multiplied by $8$, the result is the same as if the number was diminished by $6$ and the remainder multiplied by $6$. What is the number?
Printed answer:
- $14$.
verified: the printed answer passed a computed check
How it was checked
- solve: passes, with the problem read into an equation {n: 14}
On the STU-32 (STU, rpn):
```
8 GOLD x² 6 GOLD x² −
```
```
8 ENTER 6 − ÷
```
Calculator: +14E+0; the book prints 14. Run on the calculator core at firmware 628c96c.
Exercise 13, problem 5, p. 31
I have five times as many half-dollars as quarters, and the half-dollars and quarters amount to $$11$. How many of each have I?
Printed answer:
- $$4$ quarters; $20$ half-dollars.
verified: the printed answer passed a computed check
How it was checked
- solve: passes, with the problem read into an equation {q: 4, h: 20}
Exercise 13, problem 6, p. 31
A man pays a debt of $$91$ with ten-dollar bills and one-dollar bills, paying three times as many one-dollar bills as ten-dollar bills. How many bills of each kind does he pay?
Printed answer:
- $$7$ ten-dollar bills; $21$ one-dollar bills.
verified: the printed answer passed a computed check
How it was checked
- solve: passes, with the problem read into an equation {t: 7, o: 21}
Exercise 13, problem 7, p. 31
A father is four times as old as his son, but $4$ years hence he will be only three times as old as his son. How old is each?
Printed answer:
- Father, $32$ yr.; son, $8$ yr.
verified: the printed answer passed a computed check
How it was checked
- solve: passes, with the problem read into an equation {f: 32, s: 8}
Exercise 13, problem 8, p. 31
A workman was employed for $24$ days. For every day he worked he was to receive $$1.50$, and for every day he was idle he was to pay $$0.50$ for his board. At the end of the time he received $$28$. How many days did he work?
Printed answer:
- $20$.
verified: the printed answer passed a computed check
How it was checked
- solve: passes, with the problem read into an equation {w: 20}
On the STU-32 (STU, rpn):
```
0.5 ENTER 24 × 28 +
```
```
1.5 ENTER 0.5 + ÷
```
Calculator: +20E+0; the book prints 20. Run on the calculator core at firmware 628c96c.

Exercise 14

Exercise 14, problem 1, p. 32
A boy has $4$ hours at his disposal. How far can he ride into the country at the rate of $9$ miles an hour and walk back at the rate of $3$ miles an hour, if he returns just on time?
Printed answer:
- $9$ miles.
verified: the printed answer passed a computed check
How it was checked
- solve: passes, with the problem read into an equation {d: 9}
On the STU-32 (STU, rpn):
```
3 ENTER 4 ×
```
```
9 ENTER 3 + ÷
```
```
9 ×
```
Calculator: +9E+0; the book prints 9. Run on the calculator core at firmware 628c96c.
Exercise 14, problem 2, p. 32
A has $$180$, and B has $$80$. How much must A give B in order that six times B’s money shall be equal to $7$ times A’s?
Printed answer:
- $$60$.
verified: the printed answer passed a computed check
How it was checked
- solve: passes, with the problem read into an equation {x: 60}
Exercise 14, problem 3, p. 32
A grocer has two kinds of tea, one kind worth $45$ cents a pound, and the other worth $65$ cents a pound. How many pounds of each kind must he take to make $80$ pounds, worth $50$ cents a pound?
Printed answer:
- $$20$ lb. at $65$ cts.; $60$ lb. at $45$ cts.
verified: the printed answer passed a computed check
How it was checked
- solve: passes, with the problem read into an equation {x: 20, y: 60}
Exercise 14, problem 4, p. 32
A tank holding $1200$ gallons has three pipes. The first lets in $8$ gallons a minute, the second $10$ gallons, and the third $12$ gallons a minute. In how many minutes will the tank be filled?
Printed answer:
- $40$.
verified: the printed answer passed a computed check
How it was checked
- solve: passes, with the problem read into an equation {t: 40}
On the STU-32 (STU, rpn):
```
1200 ENTER 8 ENTER 10 + 12 + ÷
```
Calculator: +40E+0; the book prints 40. Run on the calculator core at firmware 628c96c.
Exercise 14, problem 5, p. 32
The fore and hind wheels of a carriage are $10$ feet and $12$ feet respectively in circumference. How many feet will the carriage have passed over when the fore wheel has made $250$ revolutions more than the hind wheel?
Printed answer:
- $15,000$.
verified: the printed answer passed a computed check
How it was checked
- solve: passes, with the problem read into an equation {D: 15000}
On the STU-32 (STU, rpn):
```
250 ENTER 10 × 12 ×
```
```
12 ENTER 10 −
```
```
÷
```
Calculator: +15000E+0; the book prints 15000. Run on the calculator core at firmware 628c96c.
Exercise 14, problem 6, p. 32
Divide a yard of tape into two parts so that one part shall be $6$ inches longer than the other part.
Printed answer:
- $15$ in.; $21$ in.
verified: the printed answer passed a computed check
How it was checked
- solve: passes, with the problem read into an equation {x: 15, y: 21}
Exercise 14, problem 7, p. 32
A boy bought $7$ dozen oranges for $$1.50$. For a part he paid $20$ cents a dozen; and for the remainder, $25$ cents a dozen. How many dozen of each kind did he buy?
Printed answer:
- $$2$ doz. at $25$ cts.; $5$ doz. at $20$ cts.
verified: the printed answer passed a computed check
How it was checked
- solve: passes, with the problem read into an equation {x: 5, y: 2}
Exercise 14, problem 8, p. 32
How can a bill of $$3.30$ be paid in quarters and ten-cent pieces so as to pay three times as many ten-cent pieces as quarters?
Printed answer:
- $$6$ quarters, $18$ ten-cent pieces.
verified: the printed answer passed a computed check
How it was checked
- solve: passes, with the problem read into an equation {q: 6, t: 18}